The importance and actuality of the Geomagnetospheres research are based on following three factors: 1. The Geomagnetosphere is the nearest giant natural Laboratory, where is possible by a lot of satellites and ground measurements investigate in details many different plasmas and energetic processes in space, caused finally by interaction of high kinetic energy solar wind plasmas and its perturbations (Interplanetary Coronal Mass Ejections ICMEs, Interplanetary Shock Waves ISWs, Interplanetary Interaction Regions IIR) with frozen in Interplanetary Magnetic Fields IMF with the rotated...